Abstract
The mechanical stretching behavior of the poly(styrene-b-ethylene-co-butylene-b-styrene) (SEBS) triblock copolymer (87 wt% polyethylene-co-butylene (PEB), 13 wt% polystyrene (PS)) was investigated under three different stretching modes and through in situ small-angle X-ray scattering (SAXS) analysis. The strain energy density function was investigated based on the stress and stretching ratio (λ) relationship under uniaxial, planar extension, and equi-biaxial stretching modes. As a result, the cross-effect of strain represented by the second invariants of the deformation tensor (I2) was identified, and only the Ogden model found to fit the data. In the cyclic stretching tests, SEBS exhibited smaller hysteresis during cyclic equi-biaxial stretching compared to uniaxial stretching. In other words, the Mullins effect was found to be more obvious for uniaxial stretching than equi-biaxial stretching. The λ and the stretching ratio obtained from the crystal planes by SAXS (λSAXS) were compared to investigate the relationship between the change in the microdomain structure and the macroscopic mechanical properties. Thus, affine deformation was found to occur in the smaller λ region for both uniaxial and equi-biaxial stretching and deviation from affine deformation occurred for uniaxial stretching in the larger λ region. This is because the entangled loops of PEB chains serve as cross-linking points when the films are stretched under equi-biaxial stretching.
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References
Treloar L. The physics of rubber elasticity. USA: Oxford University Press; 1975.
Sohn KE, Kojio K, Berry BC, Karim A, Coffin RC, Bazan GC, et al. Surface effects on the thin film morphology of block copolymers with bulk order− order transitions. Macromolecules. 2010;43:3406–14.
Tomita S, Lei L, Urushihara Y, Kuwamoto S, Matsushita T, Sakamoto N, et al. Strain-induced deformation of glassy spherical microdomains in elastomeric triblock copolymer films: simultaneous measurements of a stress–strain curve with 2d-SAXS patterns. Macromolecules. 2017;50:677–86.
Morita H, Miyamoto A, Kotani M. Recoverably and destructively deformed domain structures in elongation process of thermoplastic elastomer analyzed by graph theory. Polymer. 2020;188:122098.
Liu H, Liang X, Nakajima K. Direct visualization of a strain-induced dynamic stress network in a SEBS thermoplastic elastomer with in situ AFM nanomechanics. Jpn J Appl Phys. 2020;59:SN1013-1–6.
Dechnarong N, Kamitani K, Cheng C-H, Masuda S, Nozaki S, Nagano C, et al. In situ synchrotron radiation X-ray scattering investigation of a microphase-separated structure of thermoplastic elastomers under uniaxial and equi-biaxial deformation modes. Macromolecules. 2020;53:8901–9.
Watanabe H, Sato T, Osaki K. Concentration dependence of loop fraction in styrene−isoprene−styrene triblock copolymer solutions and corresponding changes in equilibrium elasticity. Macromolecules. 2000;33:2545–50.
Watanabe H, Matsumiya Y, Sawada T, Iwamoto T. Rheological and dielectric behavior of dipole-inverted (SIS)p-type multiblock copolymers: estimates of bridge/loop fractions for respective I blocks and effect of loops on high extensibility of bridges. Macromolecules. 2007;40:6885–97.
Takahashi Y, Song Y, Nemoto N, Takano A, Akazawa Y, Matsushita Y. Effect of loop/bridge conformation ratio on elastic properties of the sphere-forming ABA triblock copolymers under uniaxial elongation. Macromolecules. 2005;38:9724–9.
Mullins L. Effect of stretching on the properties of rubber. Rubber Chem Technol. 1948;21:281–300.
Mullins L, Tobin NR. Theoretical model for the elastic behavior of filler-reinforced vulcanized rubbers. Rubber Chem Technol. 1957;30:555–71.
Mullins L. Softening of rubber by deformation. Rubber Chem Technol. 1969;42:339–62.
Kakavas PA. Mechanical properties of bonded elastomer discs subjected to triaxial stress. J Appl Polym Sci. 1996;59:251–61.
Cho H, Mayer S, Pöselt E, Susoff M, In’t Veld PJ, Rutledge GC, et al. Deformation mechanisms of thermoplastic elastomers: stress-strain behavior and constitutive modeling. Polymer 2017;128:87–99.
Bueche F. Molecular basis for the Mullins effect. J Appl Polym Sci. 1960;4:107–14.
Obata Y, Kawabata S, Kawai H. Mechanical properties of natural rubber vulcanizates in finite deformation. J Polym Sci A-2 Polym Phys. 1970;8:903–19.
Bitoh Y, Akuzawa N, Urayama K, Takigawa T. Strain energy function of swollen polybutadiene elastomers studied by general biaxial strain testing. J Polym Sci B Polym Phys. 2010;48:721–8.
Ogden RW, Roxburgh DG. A pseudo–elastic model for the Mullins effect in filled rubber. Proc R Soc Lond A. 1999;455:2861–77.
Webber RE, Creton C, Brown HR, Gong JP. Large strain hysteresis and Mullins effect of tough double-network hydrogels. Macromolecules. 2007;40:2919–27.
Dorfmann A, Pancheri FQ. A constitutive model for the Mullins effect with changes in material symmetry. Int J Non Linear Mech. 2012;47:874–87.
Mai TT, Morishita Y, Urayama K. Novel features of the Mullins effect in filled elastomers revealed by stretching measurements in various geometries. Soft Matter. 2017;13:1966–77.
Kojio K, Matsuo K, Motokucho S, Yoshinaga K, Shimodaira Y, Kimura K. Simultaneous small-angle X-ray scattering/wide-angle X-ray diffraction study of the microdomain structure of polyurethane elastomers during mechanical deformation. Polym J. 2011;43:692–9.
McCready EM, Burghardt WR. In situ SAXS studies of structural relaxation of an ordered block copolymer melt following cessation of uniaxial extensional flow. Macromolecules. 2015;48:264–71.
Nozaki S, Masuda S, Kamitani K, Kojio K, Takahara A, Kuwamura G, et al. Superior properties of polyurethane elastomers synthesized with aliphatic diisocyanate bearing a symmetric structure. Macromolecules. 2017;50:1008–15.
Rahmawati R, Nozaki S, Kojio K, Takahara A, Shinohara N, Yamasaki S. Microphase-separated structure and mechanical properties of cycloaliphatic diisocyanate-based thiourethane elastomers. Polym J. 2019;51:265–73.
Doi T, Takagi H, Shimizu N, Igarashi N, Sakurai S. Effects of drying temperature in solution coating process on the structural changes upon uniaxial stretching of sphere-forming block copolymer films. Polym J. 2020;52:421–33.
Rahmawati R, Masuda S, Cheng C-H, Nagano C, Nozaki S, Kamitani K, et al. Investigation of deformation behavior of thiourethane elastomers using in situ X-ray scattering, diffraction, and absorption methods. Macromolecules. 2019;52:6825–33.
Shinohara Y, Kishimoto H, Masui T, Hattori S, Yamaguchi N, Amemiya Y. Microscopic structural response of nanoparticles in styrene–butadiene rubber under cyclic uniaxial elongation. Polym J. 2019;51:161–71.
Kitamura Y, Okada K, Masunaga H, Hikosaka M. Role of strain rate in the strain-induced crystallization (SIC) of natural and synthetic isoprene rubber. Polym J. 2019;51:221–6.
Shen J, Sugimoto I, Matsumoto T, Horike S, Koshiba Y, Ishida K, et al. Fabrication and characterization of elastomeric semiconductive thiophene polymers by peroxide crosslinking. Polym J. 2019;51:257–63.
Ishige R. Precise structural analysis of polymer materials using synchrotron X-ray scattering and spectroscopic methods. Polym J. 2020;52:1013–26.
Tamura E, Kume T, Okamoto S, Inoue T. A rheo-optical study on the linear viscoelasticity and molecular dynamics of block copolymer solutions forming hexagonal close-packed cylindrical domains. Polym J. 2020;52:1085–91.
Gent AN. A new constitutive relation for rubber. Rubber Chem Technol. 1996;69:59–61.
Katashima T, Urayama K, Chung U, Sakai T. Strain energy density function of a near-ideal polymer network estimated by biaxial deformation of tetra-PEG gel. Soft Matter. 2012;8:8217.
Akagi Y, Katashima T, Sakurai H, Chung U, Sakai T. Ultimate elongation of polymer gels with controlled network structure. RSC Adv. 2013;3:13251–8.
Ogden R, Hill R. Large deformation isotropic elasticity - on the correlation of theory and experiment for incompressible rubberlike solids. Proc R Soc Lond A. 1972;326:565–84.
Yohsuke B, Urayama K, Takigawa T, Ito K. Biaxial strain testing of extremely soft polymer gels. Soft Matter. 2011;7:2632–8.
Landau L, Lifshitz E. Theory of elasticity. 3rd edition. Elsevier Ltd.; 1986.
Kimishima K, Koga T, Hashimoto T. Order−order phase transition between spherical and cylindrical microdomain structures of block copolymer. I. Mechanism of the transition. Macromolecules. 2000;33:968–77.
Seguela R, Prud’homme J. Affinity of grain deformation in mesomorphic block polymers submitted to simple elongation. Macromolecules. 1988;21:635–43.
Acknowledgements
This work was supported by the Impulsing Paradigm Change through Disruptive Technology (ImPACT) Program, JST CREST Grant Number JPMJCR17J4, and JST-Mirai Program Grant Number JPMJMI18A2, Japan. Synchrotron radiation X-ray scattering measurements were performed at BL40XU and BL05XU in the SPring-8 facility with the approval of the Japan Synchrotron Radiation Research Institute (JASRI; Proposal No. 2018B1035, 2019A1015, 2019B1011, 2020A1007). ND thanks Weeradet Sittiphon for his support with the mathematical calculation. Financial support for ND was provided by the International Graduate Course on Chemistry for Molecular Systems, Ministry of Education, Culture, Sports, Science and Technology (MEXT), Japan.
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Dechnarong, N., Kamitani, K., Cheng, CH. et al. Microdomain structure change and macroscopic mechanical response of styrenic triblock copolymer under cyclic uniaxial and biaxial stretching modes. Polym J 53, 703–712 (2021). https://doi.org/10.1038/s41428-021-00469-z
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DOI: https://doi.org/10.1038/s41428-021-00469-z
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